2 Answers
2

Indirectly, yes. Gary Gygax tells us that "the mind flayer I made up out of whole cloth using my imagination, but inspired by the cover of Brian Lumley's novel in paperback edition, The Burrowers Beneath." Said novel was firmly rooted in the Cthulhu mythos; in fact, Lovecraft's character Robert Harrison Blake wrote a short story titled "The Burrower Beneath." We may suspect that title was an influence on Brian Lumley's choice of titles.

Interestingly, Lovecraft actually got the title from Robert Bloch, the writer of Psycho, who sent H.P.L. a draft of a story called "The Blasphemy Beneath". Lovecraft in turn used "The Burrower Beneath" as a title for one of Robert Blake's stories because the fictional Blake was a sort of tribute to the actual Bloch. Bloch returned the favor by making a nameless, Lovecraft-inspired character the protagonist of his own story "The Shambler from the Stars" (itself a title derived from one of Blake's fictional books).
–
Matt SheridanSep 9 '10 at 21:02

This is interesting. As a minor point: that creature will actually be a Chthonian, who is part of the Mythos, but is significantly different from Cthulhu. So the full answer would seem to be: Mind Flayers are inspired by the Cthulhu Mythos, but not by Cthulhu himself.
–
GrahamOct 25 '10 at 11:58

I think they were definitely inspired by Cthulhu, and there's no secret that the original D&D designers and fans were very familiar with the works of HP Lovecraft. It's probably not just illithids, either. We could look closely and see a lot Mythos-inspired monsters in the earliest monster manuals as well as the newest ones.